I will just quickly illustrate how I easily explain the Christian doctrine of the Trinity. I use the example of a 3 dimensional shape which casts three different shadows or profiles depending on how light is shown on it or from what axial perspective the 3d shape is viewed, and more specifically depending on from which axis the light strikes the 3d shape. It is 1 shape with 3 appearances. Similarly, God is 1 entity with 3 appearances.
Above is a picture of a sphere, a cone, and a cylinder. Viewing each shape from directly above or below, these 3d shapes will each appear as a circle. From either an X or Y axial perspective, which is to say when viewed profile from either side, there will be 3 different shapes. The sphere will still look like a circle, the cone like a triangle, and the cylinder will look like a rectangle or square, although a square is also a rectangle (the fact that a square is both a square and a rectangle is another way to conceive of God being 1 thing with 3 persons).
The shadows will show shapes just like the profile views when the light is shown along some axis. For example, when a light is cast directly down on any of these shapes it will produce a circle on a flat plane on the other side of the shape.
Now, we only need to extend this mechanism a bit so that there is a shape which can produce an additional sub-dimensional shape. Actually, we don’t even have to do this, but we will. Another approach is to say that God is a greater than 3 dimensional entity so that if 3 dimensions gets you 2 sub-dimensional shapes, maybe a 4, 5, or 6-D+ God will have 3 or more sub-dimensional shapes, or appearances from a 3D perspective. This is one approach, but we don’t actually have to do this because we can construct an irregular 3D shape which creates 3 appearances.
The shape I like is an angle-cut cylinder, but you could also use an irregular elliptical cylinder, angle-cut prisms, joint pipes, and many more.
Depending on the cylinder and the cut, one angle will appear as a circle, another angle will appear as a square or a rectangle, and the last angle will appear as a triangle or trapezoid.
This would be an even more precise comparison if God turns out to be a 4 dimensional entity because a 4 dimensional entity can have 3 dimensional shadows, but I’m not sure God is 4 dimensional and in fact God the Father and the Holy Spirit are actually immaterial, but the math demonstrates a logical system as much as a physically plausible substance.
I’ve also heard the explanation of three men who find a cow on a dark night. They can’t see it they can only feel it and they grab the cow on different parts. One describes a tail, one the face, and another the back. Who is correctly describes the cow? The cow is actually all of the above.